新手做题，求指教
数据结构与算法实验题2.1 高精度整数问题
实验任务
我们知道int 表示的数据范围是-2^31 ~ 2^31 - 1，而__int64 表示的数据范围是
-2^63~2^63 - 1。而21!就将超出__int64 的范围。
现在请你计算n!-m!的结果。
数据输入
输入数据只有一行，两个数字n 和m（0<=m<=n<=100）。
数据输出
输出n!-m!的结果。
输入示例输出示例
10 5 3628680




我写了n！-m!代码，对于超出__int64 的范围怎么看啊，求教
#include <iostream>
using namespace std;
int Factorial (int a);
int main ()
{
int n,m;
cin>>n>>m;
cout<<Factorial(n)-Factorial(m)<<endl;
}
int Factorial (int a)
{
if(a==1)
return 1;
else
return a*Factorial(a-1);
} 数据结构
[解决办法]
算法优化：n!-m! = n*...*m*...*1-m*...*1 = n*(n-1)*...*(m+2)*(m+1-1)*m*...*1
自定义大整数类（数组，一个元素放一个数位），用数组模拟笔算时的进位借位等等，自己算出结果，然后再将结果数组从高位到低位依次打印到输出界面

如果这道题用你写的那点代码就能完成，那这算哪门子的“数据结构与算法实验题”？
[解决办法]

#include <iostream>
#include <string>
#include <algorithm>
using namespace std;
int COMPARE(string number1, string number2) {
    int i,j;

    int length1 = number1.size();
    int length2 = number2.size();

    if(number1.size() == 0) number1 = "0";
    if(number2.size() == 0) number2 = "0";

    j = 0;
    for(i = 0; i < length1; ++i) {
        if(number1[i] == '0') ++j;
        else break;
    }
    number1 = number1.substr(j);

    j = 0;
    for(i = 0; i < length2; ++i) {
        if(number2[i] == '0') ++j; 
 
        else break;
    }
    number2 = number2.substr(j);

    length1 = number1.size();
    length2 = number2.size();

    if(length1 > length2) {
        return 1;
    } else if(length1 == length2) {
        if(number1.compare(number2) > 0) {
            return 1;
        } else if(number1.compare(number2) == 0) {
            return 0;
        } else {
            return -1;
        }
    } else {
        return -1;
    }

    return 0;
}
string PLUS(string number1,string number2) {
    int i;
    int length1 = number1.size();
    int length2 = number2.size();

    string result="";

    reverse(number1.begin(), number1.end());
    reverse(number2.begin(), number2.end());

    for(i = 0; i < length1 && i < length2; i++) {
        char c = (char)(number1[i] + number2[i] - 48);
        result = result + c;
    }

    while(i < length1) {
        result = result + number1[i];
        ++i;
    }

    while(i < length2) {
        result = result + number2[i];
        ++i;
    }

    int carry = 0;
    for(i = 0; i < (int)result.size(); ++i) {
        int value = result[i] - 48 + carry; 
 
        result[i] = (char)(value % 10 + 48);
        carry = value / 10;
    }

    if(carry !=0 ) {
        result = result + (char)(carry + 48);
    }

    for(i = result.size() - 1; i >= 0; i--) {
        if(result[i] != '0') break;
    }

    result = result.substr(0, i + 1);

    reverse(result.begin(), result.end());
    if(result.length() == 0) result = "0";
    return result;
}
string MINUS(string number1,string number2) {
    int i;
    string result = "";

    int length1 = number1.size();
    int length2 = number2.size();

    if(COMPARE(number2,number1) > 0) {
        return "-" + MINUS(number2, number1);
    }

    reverse(number1.begin(),number1.end());
    reverse(number2.begin(),number2.end());

    for(i = 0; i < length1 && i < length2; i++) {
        char c = number1[i] - number2[i] + 48;
        result = result + c;
    }

    if(i < length1) {
        for(; i < length1; i++) {
            result = result + number1[i];
        }
    }

    int carry = 0;
    for(i = 0; i < (int)result.length(); i++) {
        int value = result[i] - 48 + carry;
        if(value < 0) {
            value = value + 10; 
 
            carry = -1;
        } else carry = 0;
        result[i]=(char)(value + 48);
    }

    for(i = result.size() - 1; i >= 0; i--) {
        if(result[i] != '0')break;
    }

    result = result.substr(0, i+1);

    reverse(result.begin(), result.end());
    if(result.length()==0) result = "0";
    return result;
}
string MULTIPLY(string number1, string number2) {
    int i, j;
    int *iresult;
    int length1 = number1.size();
    int length2 = number2.size();
    string result = "";

    reverse(number1.begin(), number1.end());
    reverse(number2.begin(), number2.end());

    iresult = (int*)malloc(sizeof(int) * (length1 + length2 + 1));
    memset(iresult, 0, sizeof(int) * (length1 + length2 + 1));

    for(i = 0; i < length1; i++) {
        for(j = 0; j < length2; j++) {
            iresult[i+j] += ((number1[i] - 48) * (number2[j] - 48));
        }
    }

    int carry = 0;
    for(i = 0; i < length1 + length2; i++) {
        int value = iresult[i] + carry;
        iresult[i] = value % 10;
        carry = value / 10;
    }

    for(i = length1 + length2 - 1; i >= 0; i--) {
        if(iresult[i] != 0)break;
    }

    for(; i >= 0; i--) {
        result = result + (char)(iresult[i]+48); 
 
    }

    free(iresult);

    if(result == "") result = "0";
    return result;
}
string factorial(string n) {
    string temp = "1";
    string i;
    for(i = "1"; COMPARE(i, n) <= 0; i = PLUS(i, "1")) {
        temp = MULTIPLY(temp, i);
    }
    return temp;
}
int main(void) {
    cout << factorial("100") << endl;
    return 0;
}